and their relation to the Velocities of Currents. 193 
ripple produced by the oblique jet should be exactly 5 inches 
distant from the axis. Theoretically, the ripple corresponding 
to the vertical jet should then have been the znvolute of a circle 
(art. 13); in reality, however, the ripple was scarcely distin- 
guishable in such cases, the disturbance which the vertical jet 
produced upon the surface of the water‘in the bath being still 
so small. 
28. Although the apparatus was sufficiently delicate to esta- 
blish the fact of slight variations in the velocity X due to differ- 
ences in the obliquity of the jet and the velocity of efflux, it did 
not appear suitable for the full investigation of the magnitude and 
conditions of these variations; I contented myself therefore with 
a few determinations of X from a series of observations made 
under all possible conditions. From them the limits of the varia- 
tion of X may be to some extent ascertained and its mean value 
estimated. In order to calculate X from the data supplied by 
experiment, the formula 
Ai 
fon 
given in art. 20, requires a slight transformation. The circum- 
ference of the circle described by the jet being 27ra, and n rota- 
tions being made in ¢ seconds, the velocity u has the value 
Qcran 
— r 3 
so that the above equation giving the velocity X per second 
becomes 
27r 
A= 2. ° pi Matias Woe Yk tates (4:2) 
According to this, and as already hinted in the last article, the 
velocity X depends, solely, upon the number of rotations in a 
given time, and upon the distance r of the cusp of the ripple 
from the axis of the instrument; in other words, it is not de- 
pendent upon the radius of the circle described by the jet; so 
that it was not necessary to determine the distance, from the 
axis, of the point of impact between the jet and the water in the 
bath, and therefore not necessary to ascertain the height of the 
water in the bath, or to render the latter constant. 
29. Some of the results of a great many accordant observa- 
tions are shown in the following Table, wherein 2 represents the 
number of rotations per minute, 7 the distance (in inches) from 
the axis of the cusp of the ripple, and X the velocity in inches 
per second with which the corresponding waves are propagated, 
calculated according to (42) :— 
Phil. Mag. 8. 4. Vol. 21. No. 189, March 186}. O 
